Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913496378114048 |
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| author | Kozik, Evgeny |
| author_facet | Kozik, Evgeny |
| contents | Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_13774 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model Kozik, Evgeny Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods. |
| title | Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2309.13774 |